这是描述插图和示威的汉密尔顿范式理论,它限制扰动和解释是齐次多项式的正则变换(p.88桑德斯et al .,2007)。同样,研究概念也有助于确定的技术,可以用来改变正常的微分方程,并将非线性动力系统转换为特定的标准形式。因此,通过利用特定类的同步转换,可以减少在高阶非线性的无关紧要的部分同样被发现重要的实现想要的结果。
Including averaging over angle methods in this study, it helps in allowing the estimation of the problem that are based on vector or tensor Laplace equation through the problem based on a scalar Laplace equation. Likewise, the technique of second order differential equation was also helpful in the demonstration of the situation when non-linear ordinary differential equation is derived two times in relation to its differential variable. Moreover, it was also revealed that the use of the periodic case can be made for the higher-order approximations mostly, that further assist in formulation of the developed theory with different forms (Arrowsmith & Place, 1990, p.352).
It was depicted from the illustrations and demonstrations of the Hamilton Normal Form Theory that it confines the perturbations and explanations to be the homogeneous polynomials to the canonical transformation (Sanders et al., 2007, p.88). Likewise, the studied concept also helped in the determination of the techniques that can be used to alter the normal differential equations that demonstrates and converts the non-linear dynamical systems into the specific standard forms. Therefore, by utilization of the specific class of synchronized transformation, the reduction can be made in the insignificant parts of higher order non-linearities as the same was found significant in achieving the desired outcomes.
Hence, it can be concluded that the identified differential equation can depict the solutions with respect to the integrals used in the function of Asymptotic Approximations.